Wave filter



Oct. 1, 1940. H. G. ocH 2,216,541

WAVE FILTER Filed Sept. 24,. 1938 A TTORNE V Patented Oct. 1, 1940 UNITED; s'mrriasV PATENT OFFICE- WAVE FILTER Application September 24, 1938, Serial No. 231,492

12 Claims.

This invention relates to wave transmission networks and more particularly to wave lters in which piezoelectric crystals are used as impedance elements.

An object of theinvention is to increase the width of the transmission band in a wave lter employing piezoelectric crystals. Another object is to increase the range or ranges of sustained high attenuation in such a filter.

.It is known how to build a band-pass wave filter which uses piezoelectric crystals and has a limited band width and a limited number of attenuation peaks. In accordance with the present invention there is provided a crystal band lter in which the band may be extended to any desired width and which has any desired number of arbitrarily placed attenuation peaks. By providing a sufcient number of peaks and by properly choosing their locations the attenuation of the iilter may be kept ata sustained high value over any desired frequency range or ranges.

The lter is a symmetrical lattice network and each branch of the lattice comprises two or more piezoelectric crystals, with an individual inductorv associated with each crystal. If the crystal and the inductor are connected in series, the combinations are connected in parallel. In order to facilitate the placing of the frequency of antiresonance for the combination, a capacitor, which may be made variable, is usually connected in parallel with the crystal.

If each branch of the lattice has two crystals the transmission band of the lter may be. made more than twice the width heretofore attainable with crystal lters. Furthermore, the filter may be designed to have seven peaks of attenuation which may be placed at arbitrarily chosen frequencies, all on one side of the band or part below and part above the band. Additional peaks may be provided and the band may be further widened by using more crystals. added crystal and its associatedinductor will provide four more peaks of attenuation. Some of the available critical frequencies may be utilized to improve the image impedance of the ilter in the transmission band, in which case the number of attenuation peaks. will be correspondingly reduced. However, by using' a sufficient number of crystals and associated reactance elements any desired number of peaks may beprovided.

The nature of the` invention will bev more fully understood from the following detailed description and by reference to the accompanying drawing of which:

Fig. l is a schematic circuit showing a. band.-

In general eachk pass wave filter in accordance with the invention;

Fig. 2 represents an equivalent electrical circuit for a piezoelectric crystal element;

Fig. 3 shows an equivalent electrical circuit for` one of the impedance arms of Fig. 1;

Fig. 4 shows an electrical circuit which is equivalent to that shown in Fig. 3;

Fig. 5 shows a lattice network which is equiva-. lent to the lter circuit of Fig. 1;

Fig. 6 shows the reactance-frequency characteristics for the branches of the lattice networks of Figs. 1 and 5; and

Fig. 7 represents a typical attenuation characteristic for the filter.

Fig. l is a schematic circuit of a band-pass wave lter in accordance with the invention. The network comprises two similar line impedance branches Z1 and two similar diagonal impedance` branches Z2 disposed between a pair of input terminals l, 2 and a pair of output terminals 3, 4 to form a symmetrical lattice structure. Each impedance branch includes two piezoelectric crystals and their associated inductors and capacitors. For the sake of clarity in this gure and also in Fig. 5 only one line branch and one diagonal branch are shown in detail, thev other corresponding line and diagonal branches being inclicated by dotted lines connecting the appropriate terminals. f

Each line impedance branch Z1 of the lattice comprises two parallel arms 5 and 6, one made up of a piezoelectric crystal X1 in series with an. inductor LX1 and shunted by a capacitor Cx1, and the other consisting of a crystal X3 in series' with an inductor Lxz and shunted by a capacitor 0X3. Each diagonal branch Z2 is of the samestructure as the line branches and comprises two parallel arms 'I and 8, one made up of a crystal X2 in series with an inductor Lxz and shunted by a capacitor Cxz, and the other consisting of a .crystal X4 in series with an inductor LXA and shunted by a capacitor CX4. The capacitors may be made variable, as indicated by the arrows, so that the anti-resonances of the crystal-capacitor combinations may be readily adjusted to the required frequencies.

As shown in Fig. 2, an equivalent electrical cir-- cuit representing a piezoelectric crystal element including its associated electrodes comprises a capacitance CE shunted by a branch consisting of an inductance LA in series with afcapacitance CA. The capacitance CE is the simple electrostatic capacitance between the electrodes of ther crystal. The values of the inductance LA and the. capacitance. CA depend upon the dimensionsl of the crystal and upon its piezoelectric and elastic constants. These elements may be evaluated from formulas readily available.

If Fig. 2 is taken as representing the equivalent circuit for the crystal X1 then the equivalent circuit for the arm 5 in Fig. 1 Will be as shown `in Fig. 3, in which the capacitance CB is equal to the sum of the capacitances CE and Cx1. Now the circuit of Fig. 3 may be transformed into the circuit shown in Fig. 4 comprising two parallel arms 9 and IIJ, one made up of an inductance L1 in series with a capacitance C1, and the other consisting of an inductance La in series with a capacitance Ca. The formulas required for this transformation are given in connection with Fig. 13 in Appendix D of K. S. Johnsons Transmission Circuits for Telephonic Communication, published by D. Van Nostrand Company.

In like manner the other arms 6, l and 8 of Fig. 1 may be transformed into equivalent circuits of the type shown in Fig. 4'. The complete lattice network equivalent to the lattice of Fig. l will then be as shown in Fig. 5. The line branch Z1 consists of four resonant arms 9, I9, II and I2 connected in parallel, and the diagonal branch Z2 comprises four other resonant arms I3, I4, I5 and I5 also connected in parallel. The subscripts on the reference letters denoting the reactance elements indicate the frequencies of resonance of the various arms.

The reactance-frequency characteristic for the line branch Z1 will be as shown by the solid-line curve of Fig. 6, having zeroes at the frequencies f1, f3, f5 and f1, and poles at the frequencies f2, f4 and fe. The diagonal branch will have a reactance characteristic of the same type, as shown by the dotted-line curve. In order to provide a band-pass lter the zeroes and poles of one branch are made to coincide with the poles and zeroes, respectively, of the other branch. There- `fore, as shown in Fig. 6, the diagonal branch has zeroes at f2, f4, fs and faz, and poles at f3, f5 and f7. The diagonal branch has no pole at f1 corresponding to the zero of the line branch at vthis frequency, and the line branch has no pole Aat fa corresponding to the zero of the diagonal branch. The frequencies f1 and f8 will therefore determine the limits of the transmission band, which will extend between these frequencies.

The lter shown will ordinarily have seven peaks of attenuation and these may be placedV all on'either side of the band, or part on one sideand part on the other. The peaks occur where the two impedances Z1 and Z2 are equal, and in Fig. 6 three such frequencies, fa, fb and fc, are

found below the band and four, fs, fio, f11 and fiz, above. The location of these peaks is determined by the distribution of the critical frequencies within the transmission band and these are generally so chosen that the attenuation is maintained above some required minimum values over the desired frequency ranges on each side of the band. Fig. 'l shows a typical attenuation char- Bell System Technical Journal, vol. III, No. 2, April, 1924, pages 259 to 267. The arm 9 consisting of L1, C1 having the lowest resonance and the arm I comprising L3, C3 having thev next higher resonance in the line branch are now grouped together to form the circuit shown in Fig. 4. This circuit is then transformed into the equivalent circuit of` Fig. 3 by means of the formulas given in Johnsons book mentioned above. Thevalue of the inductance Lx1 in the arm of Fig. 1 is thus found. 'Ihe values of the inductance LA and the capacitance CA in the equivalent electrical circuit representing the crystal X1, as given in Fig. 2, are also determined. The dimensions of the crystal X1 having the required resonance frequency can then be calculated, and the value of the electrostatic capacitance CE computed. The value of the capacitance Cx1 to be added in shunt with the crystal will be the difference between CB and CE.

All of the elements X1, Cx1 and LX1 in the arm 5 of Fig. 1 have thus been fixed, and zthis arm is equivalent to the two parallel arms 9 and IIJ of Fig. 5. and I2 in the line branch Z1 of Fig. 5 are converted into the equivalent arm 6 of Fig. 1. In the same way the arms I3,V I4 and I5, I6 in the diagonal branch Z2 of Fig. 5 are converted into the equivalent arms 'I and 8 of Fig. 1. The values of all of the component elements in the circuit of Fig. 1 have now been determined.

The transmission band of the lter may be further widened and additional peaks of attenuation may be provided by adding more crystals, with their associated inductors and capacitors. In general the addition of a crystal and its associated reactance elements to each impedance branch of the lattice of Fig. 1 will add four more peaks. When required some of the critical frequencies may be placed outside of the transmission band and used to improve the image impedance of the filter, with a consequent reduction in the number of attenuation peaks. However, the transmission band may be widened to any desired extent and any number of peaks may be provided if a suflicient number of crystals and reactance elements are used.

What is claimed is:

'1. A wave filter comprising four impedance branches equal in pairs and disposed between in- 1 put terminals and ouput' terminals to form a symmetrical lattice network, each of said branches comprising a plurality of impedance combinations, each of said impedance combinations including a piezoelectric crystal and an associated inductor, and said pairs of branches having diierent reactance-frequency characteristics proportioned'with respect to each other to provide a single transmission band.

2. A wave iilter in accordance with claim 1 in which each of said inductors is connected in series with its associated crystal.

3. A wave filter in accordance with claim 1 in which all of said impedance combinations in each of said branches are connected in parallel.

4. A Wave filter in accordance Withclaim 1 in which each of said inductors is connected in series with its associated crystal and all of said impedance combinations in each of said branches are connected in parallel.

5. A wave lter in accordance with claim 1 which includes added capacitors connected in shunt with certain of said crystals.

6. A wave lter comprising four impedance branches equal in. pairs and disposed between In like manner the remaining arms II input terminals and output terminals to form a symmetrical lattice network, each of one of said pairs of branches comprising a plurality of impedance combinations connected in parallel, each of said impedance combinations including a piezoelectric crystal and an inductor connected in series, each of the other of said impedance branches comprising a plurality of other impedance combinations, ea-ch of said other impedance combinations including a piezoelectric crystal and an associated inductor, and said pairs of branches having different reactance-frequency characteristics proportioned with respect to each other to provide a single transmission band.

7. A Wave lter in accordance With claim 6 which includes added capacitors connected in shunt with certain of said crystals.

8. A Wave lter comprising four impedance branches equal in pairs and disposed between input terminals and output terminals to form a symmetrical lattice network, each of said branches comprising a plurality of parallel paths, each of said paths including a piezoelectric crystal and an associated inductor connected in series, and said pairs of branches having different reactance-frequency characteristics proportioned with respect to each other to provide a single transmission band.

9. A Wave lter in accordance with claim 8 in which certain of said paths include added capacitors connected in shunt with said crystals.

10. A Wave lter in accordance with claim 8 in Which each of said paths includes an added capacitor connected in shunt with the crystal in said path.

11. A Wave filter in accordance with claim 1,

Which includes added capacitors connected in` shunt with certain of said crystals and in which each of said inductors is connected in series with its associated crystal.

12. A Wave lter in accordance with claim 1, which includes added capacitors connected in shunt with certain of said crystals and in which all of said impedance combinations in each of said branches are connected in parallel.

HENRY G. OCH. 

